Maharashtra State BoardHSC Arts 12th Board Exam
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Solve the following differential equation: dydxyxdydx=(1+y)2(1+x)2 - Mathematics and Statistics

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Sum

Solve the following differential equation:

`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`

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Solution

`"dy"/"dx" = (1 + "y")^2/(1 + "x")^2`

∴ `1/(1 + "y"^2) "dy" = 1/(1 + "x"^2) "dx"`

Integrating both sides, we get

`int 1/(1 + "y"^2) "dx" = int1/(1 + "x"^2) "dx"`

∴ tan-1 y = tan-1 x + c

This is the general solution.

Concept: Formation of Differential Equations
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